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Sequential Conditional Transport on Probabilistic Graphs for Interpretable Counterfactual Fairness
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Extends Knothe-Rosenblatt and triangular transport to probabilistic causal graphs to build closed-form sequential conditional transport counterfactuals, and applies them to individual and aggregate counterfactual fairness on synthetic and real data.
Problem
Constructing counterfactuals for individual counterfactual fairness that respect a known causal DAG, where existing optimal-transport counterfactuals are hard to implement and interpret for non-Gaussian data.
Approach
Combine causal-graph counterfactuals with optimal transport by applying univariate conditional monotone transport maps in topological order of the DAG (sequential transport), yielding closed-form, interpretable, out-of-sample-applicable counterfactuals rather than a joint multivariate OT map.
Key results
- On the Law School dataset, sequential transport gives aware-model CDP of 0.3723 versus 0.3727 for multivariate OT and 0.3810 for Fairadapt.
- On the Law School dataset, sequential transport gives unaware-model CDP of 0.1817 versus 0.1821 for multivariate OT and 0.1918 for Fairadapt.
- On the simulated example, the counterfactual score for an individual is 61.40% under one causal graph and 56.34% under another, versus 56.5% for multivariate OT.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use sequential transport instead of Fairadapt | Aware logistic regression · Law School Admission Council (Black individuals) | CDP: 0.3810 -> 0.3723 | No clear effect |
| Use sequential transport instead of multivariate OT | Aware logistic regression · Law School Admission Council (Black individuals) | CDP: 0.3727 -> 0.3723 | No clear effect |
| Use sequential transport instead of Fairadapt | Unaware logistic regression · Law School Admission Council (Black individuals) | CDP: 0.1918 -> 0.1817 | No clear effect |
| Use sequential transport instead of multivariate OT | Unaware logistic regression · Law School Admission Council (Black individuals) | CDP: 0.1821 -> 0.1817 | No clear effect |
| Exclude sensitive attribute s from the classifier features | Sequential transport logistic regression · Law School Admission Council (Black individuals) | CDP: 0.3723 -> 0.1817 | Helped |
Surprising findings
- The aware logistic model, which includes the sensitive attribute, is less counterfactually fair than the unaware model.
Limitations
- Categorical variables break the atomless existence/uniqueness guarantees, requiring a multinomial sampling heuristic.
- Results depend on the assumed causal graph; edge misspecification affects counterfactuals.
Experimental setup
Datasets: Law School Admission Council dataset adult income (UCI) COMPAS German Credit synthetic data
Benchmarks: Law School Admission Council dataset adult income COMPAS
Metrics: counterfactual demographic parity (CDP) counterfactual equality of opportunity counterfactual class balance counterfactual equal treatment
Baselines: Fairadapt multivariate OT naive ceteris paribus counterfactual
Builds on: Knothe-Rosenblatt rearrangement triangular transport Fairadapt multivariate optimal transport counterfactuals
Closest papers by meaning
- Interventional Fairness on Partially Known Causal Graphs: A Constrained Optimization Approach (ICLR 2024 · similarity 0.85)
- Counterfactual Graphical Models: Constraints and Inference (ICML 2025 · similarity 0.85)
- A Comprehensive View of Fairness through Distributional Stability (NeurIPS 2026 · similarity 0.84)
- A Generic Framework for Conformal Fairness (ICLR 2025 · similarity 0.84)
- Causal Abstractions, Categorically Unified (NeurIPS 2026 · similarity 0.84)
- Fairness on Principal Stratum: A New Perspective on Counterfactual Fairness (ICML 2025 · similarity 0.84)
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